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New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution.
Acta Crystallographica Section A: Foundations and Advances ( IF 1.9 ) Pub Date : 2020-04-28 , DOI: 10.1107/s2053273320003794 V G Kohn 1 , I A Smirnova 2
Acta Crystallographica Section A: Foundations and Advances ( IF 1.9 ) Pub Date : 2020-04-28 , DOI: 10.1107/s2053273320003794 V G Kohn 1 , I A Smirnova 2
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The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.
中文翻译：
在Borrmann效应条件下，在具有不均匀出射面的单晶中进行X射线Laue衍射时的新型干涉。分析解决方案。
推导了出射面厚度线性变化的单晶中X射线球面劳厄衍射问题的解析解。一般方程适用于在Borrmann效应条件下厚晶体中平面波劳厄衍射的特定情况。结果表明，如果在反射光束的侧面增加厚度，则相关的反射波振幅将作为三项之和来计算，其中两项是复数。如果所有三个项都具有可比较的模量，则与晶体的平面平行形状的值相比，由于干扰，它可能导致反射光束强度最多增加9倍。相关的透射波振幅的方程式仅包含两个项。因此，与反射光束相比，增加强度的可能性较小。在通过Laplace变换对积分方程进行求解之后，获得了解析解。使用了较早推导的Takagi方程的一般积分形式。通过解析方程计算相对强度的结果与直接计算机模拟的结果相吻合。
更新日期：2020-04-28
中文翻译：
在Borrmann效应条件下，在具有不均匀出射面的单晶中进行X射线Laue衍射时的新型干涉。分析解决方案。
推导了出射面厚度线性变化的单晶中X射线球面劳厄衍射问题的解析解。一般方程适用于在Borrmann效应条件下厚晶体中平面波劳厄衍射的特定情况。结果表明，如果在反射光束的侧面增加厚度，则相关的反射波振幅将作为三项之和来计算，其中两项是复数。如果所有三个项都具有可比较的模量，则与晶体的平面平行形状的值相比，由于干扰，它可能导致反射光束强度最多增加9倍。相关的透射波振幅的方程式仅包含两个项。因此，与反射光束相比，增加强度的可能性较小。在通过Laplace变换对积分方程进行求解之后，获得了解析解。使用了较早推导的Takagi方程的一般积分形式。通过解析方程计算相对强度的结果与直接计算机模拟的结果相吻合。
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